A numerical point of view at the Gurov-Reshetnyak inequality on the real line

TL;DR

This paper computes the norm of a power function in the Gurov-Reshetnyak class on the real line and provides a numerical lower bound for the extension operator from the semi-axis to the entire real line.

Contribution

It offers a numerical analysis of the Gurov-Reshetnyak class norms and introduces a new lower bound for the extension operator based on numerical experiments.

Findings

Computed the norm of power functions in the Gurov-Reshetnyak class.

Established a numerical lower bound for the extension operator.

Provided insights into the behavior of the extension operator on the real line.

Abstract

A "norm" of power function in the Gurov-Reshetnyak class on the real line is computed. Moreover, a lower bound for the norm of the operator of even extension from the semi-axis to the whole real line in the Gurov-Reshetnyak class is obtained from numerical experiments.